Binary to Octal Converter
Convert long binary strings to octal notation efficiently. Features automatic 3-bit chunking, clipboard sanitization, and handling of large bitstreams for systems architecture.
About
System architects and Unix administrators frequently handle file permissions and raw data streams where compactness is essential. While binary represents the raw machine state, octal (base-8) offers a concise representation by grouping bits into triplets. This tool bridges the gap, allowing for the rapid conversion of extended binary sequences into octal format without manual calculation errors. Accuracy is paramount when configuring chmod settings or interpreting legacy computing data, as a single bit shift can alter read/write privileges or corrupt data interpretation.
The converter utilizes a chunking algorithm that strictly enforces the mathematical relationship where 3↔1 (three binary digits map to exactly one octal digit). It handles input sanitization automatically, stripping whitespace and formatting irregularities often introduced by copy-pasting from terminal outputs or documentation.
Formulas
The conversion process relies on partitioning the binary string into groups of three, starting from the least significant bit (right to left). If the total number of bits is not divisible by three, leading zeros are added to the most significant end (left padding).
For a binary triplet b2b1b0, the octal value O is calculated as:
O = b2 × 22 + b1 × 21 + b0 × 20
Example for 101:
1 × 4 + 0 × 2 + 1 × 1 = 5
Reference Data
| Binary (3-bit) | Octal Digit | Unix Permission Equivalent |
|---|---|---|
| 000 | 0 | No permissions (---) |
| 001 | 1 | Execute only (--x) |
| 010 | 2 | Write only (-w-) |
| 011 | 3 | Write & Execute (-wx) |
| 100 | 4 | Read only (r--) |
| 101 | 5 | Read & Execute (r-x) |
| 110 | 6 | Read & Write (rw-) |
| 111 | 7 | Read, Write & Execute (rwx) |
| 111 101 101 | 755 | Owner: rwx, Group: r-x, Others: r-x |
| 110 100 100 | 644 | Owner: rw-, Group: r--, Others: r-- |